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A287688
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Triangle read by rows: T(j,k) is the number of distinct edge segment pairs in a j X k rectangular grid.
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2
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2, 6, 7, 10, 15, 13, 15, 21, 28, 22, 21, 28, 36, 45, 32, 28, 36, 45, 55, 66, 45, 36, 45, 55, 66, 78, 91, 59, 45, 55, 66, 78, 91, 105, 120, 76, 55, 66, 78, 91, 105, 120, 136, 153, 94, 66, 78, 91, 105, 120, 136, 153, 171, 190, 115, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 137
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OFFSET
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1,1
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COMMENTS
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This gives the number of pairs of edge segments that are distinct with respect to rotation and mirror images. Sequence is arranged so that j <= k (since 2 X 3 and 3 X 2 are equivalent grids), first by increasing j, then by increasing k: a(1) = 1 X 1 = 2, a(2) = 1 X 2 = 6, a(3) = 2 X 2 = 7, a(4) = 1 X 3 = 10.
Where j != k, a(n) = A000217(j + k).
Where j = k, a(n) is approximately A236312(j-2); a(n) >= A236312(j-2).
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LINKS
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EXAMPLE
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Triangle begins:
2;
6, 7;
10, 15, 13;
15, 21, 28, 22;
21, 28, 36, 45, 32;
28, 36, 45, 55, 66, 45;
36, 45, 55, 66, 78, 91, 59;
...
For n = 3, the a(3) = 7 pairs of edge segments for a 2 X 2 rectangular grid are:
+ - - + + * * + + * - + + * - + + * - + + * - + + * - + + * - +
| | --\ | | | * | | | | | | | | * |
| | --/ | | | | | * | | | | * | | |
+ - - + + - - +, + - - +, + - - +, + - * +, + * - +, + - - +, + - - +.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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